Abstract
The paper presents the theory of the discontinuous Galerkin finite element method for the space-time discretization of a nonstationary convection-diffusion initial-boundary value problem with nonlinear convection and linear diffusion. The problem is not singularly perturbed with dominating convection.
The discontinuous Galerkin method is applied separately in space and time using, in general, different space grids on different time levels and different polynomial degrees p and q in space and time dicretization. In the space discretization the nonsymmetric, symmetric and incomplete interior and boundary penalty (NIPG, SIPG, IIPG) approximation of diffusion terms is used.
The paper is concerned with the proof of error estimates in L2(L2)- and DG-norm formed by the L2(H1)-seminorm and penalty terms. A special technique based on the use of the Gauss-Radau interpolation and numerical integration has been used for the derivation of an abstract error estimate.